Abstract 

In 1957, D. A. Burgess made a spectacular breakthrough on bounding short character sums, going way beyond the earlier work of Polya and Vinogradov. His result had major applications, in particular to Dirichlet L-functions, the distribution of prime numbers in arithmetic progressions and the structure of nite elds. Going beyond Burgess' achievement remains a major challenge today. The first aim of this talk is to review Burgess argument, which is based on several distinct ingredients, especially the work of A. Weil. Next, we present some more recent developments of these ideas. We will present results on incomplete character sums over general nite elds and multilinear character sums, where analogues of Burgess theorem can be proven. The problems considered go back to Davenport-Lewis and Burgess himself. The new input will be of a more combinatorial nature.
 

About the speaker

Mei-Chu Chang is a professor of mathematics at University of California at Riverside. Her earlier work is in algebraic geometry and her present research relates to combinatorial number theory and discrete math. She got her bachelor's degree from National Taiwan University, and PhD from UC Berkeley under Hartshorne. Before she joined UC Riverside, she was a Bateman Instructor at California Institute of Technology, a visiting assistant professor at the University of Michigan, and a postdoc at UCLA. She also spent time at IHES, Mittag-Leffler, University of Rome and was a member at IAS. She was a plenary speaker at an AMS meeting , an invited speaker at many research institutions and recently a plenary speaker at the 9th International Conference on Finite Fields and their Applications in Dublin.

Free and open to the public. Seating is on a first-come first-served basis.

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